A036417 -id:A036417 - cp's OEIS frontend

A036416 Number of empty intervals when fractional_part(i*Pi) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.

0, 1, 1, 1, 1, 0, 0, 1, 2, 3, 4, 4, 5, 7, 7, 7, 8, 9, 10, 11, 14, 12, 12, 14, 13, 14, 16, 21, 15, 17, 18, 16, 18, 19, 21, 20, 20, 21, 20, 22, 22, 23, 21, 22, 22, 23, 24, 25, 27, 21, 24, 24, 23, 25, 25, 28, 22, 25, 24, 26, 25, 25, 27, 21, 25, 24, 26, 24, 25, 25, 21, 24, 22, 23, 22

Offset: 1

Eric W. Weisstein

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Equidistributed Sequence.

Cf. A036417 (positions of 0).

Cf. similar sequences with other constants: A036412 (e), A036414 (phi), A046157 (gamma).

Table[Length@Complement[Range[n] - 1, Floor[n*FractionalPart[Pi*Range[n]]]], {n, 75}] (* Ivan Neretin, Jan 23 2018 *)

A046158 Values of n for which there are no empty intervals when frac(m*gamma) for m = 1, ..., n is plotted along [0, 1] subdivided into n equal regions.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 12, 19, 26, 97, 123, 149, 272, 395, 5258, 5653, 26685, 31943, 58628, 500967, 559595

Offset: 1

Eric W. Weisstein

No others with n <= 10^6. - Eric W. Weisstein, Apr 26 2024

Eric Weisstein's World of Mathematics, Equidistributed Sequence
Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant

Cf. A046157.
Cf. A046115 (denominators of the convergents to the Euler-Mascheroni constant).
Corresponding sequences for other constants: A036413 (e), A036415 (phi), A036417 (Pi).

With[{f = FractionalPart[EulerGamma Range[1000]]}, Position[Table[Count[BinCounts[Take[f, n], {0., 1, 1/n}], 0], {n, Length[f]}], 0]] // Flatten (* Eric W. Weisstein, Apr 27 2024 *)

a(19) from Sean A. Irvine, Nov 01 2020

a(20)-a(21) from Eric W. Weisstein, Apr 26 2024

cp's OEIS Frontend

A036416 Number of empty intervals when fractional_part(i*Pi) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.

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